A more flexible approach would be to learn the natural image statistics using a generative model and use it for solving various inverse problems.
Recently, deep generative models especially using autoregressive framework [1]}, [2]}, [3]} have led to state-of-the-art performance in modeling natural image manifold. Autoregressive models factorize the image distribution as a 2D directed causal graph and hence model it as a 2-D sequence where current pixel's distribution is conditioned on the causal context.
By employing deep neural networks for summarizing the causal context, autoregressive models excel at capturing long range dependencies in images. Also, being a pixel level model it explicitly accounts for higher order correlations like texture patterns, sharp edges, etc. within a neighbourhood. Thus, these models are capable of generating visually convincing and crisp images [1]}. Examples of deep autoregressive image models are recurrent image density estimator (RIDE) [2]}, pixel recurrent neural networks (PixelRNN) and its CNN equivalent (PixelCNN) [1]} and PixelCNN++ [3]}.
